She also has a good shot because her qualifications are similar to the few kids (all males) who got into CMU SCS from our school last year.
No. CMU will recognize your math talent based upon your AIME score and other math competitions. They know that SAT math is trivial by comparison. If you didn’t have that, then I would have recommended a retake.
A quick note about CMU culture: Dig into the CMU SCS culture and make sure it is right for you. While it is, IMO, the best CS program in the nation, the culture is not right for everyone.
Are you also applying EA to Michigan and Ga Tech?
Yes you do. A much better chance there than at Stanford. This is anecdotal, but demonstrated interest seems to matter to CalTech. Our high school admits a student to CalTech every few years, and for the most recent one a couple of years ago, CalTech chose the student who visited over stronger students that did not.